Y. Sun and J. Xin (USA)
Signal reconstruction, digital signal processing, unique solvability, geometric method.
We study the unique solvability of sparse blind separation of n non-negative sources from m linear mixtures in the under-determinedregime m < n. Such source signals arise in nuclear magnetic resonance data. The geometric proper ties of the mixture matrix and sparseness structure of source matrix are closely related to the unique identification of the mixing matrix. We illustrate and establish necessary and sufficient conditions for the unique separation up to scaling and permutation. We also present a novel algorithm based on data geometry, source sparseness, and l1 minimization. Numerical results substantiate the uniqueness of the source signal recovery, and show satisfactory performance of our algorithm on chemical data.
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